Precalculus Examples

$\log_{5} (500) - 2 \log_{5} (2)$

Step 1

Simplify each term.

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Step 1.1

Simplify $- 2 \log_{5} (2)$ by moving $2$ inside the logarithm.

$\log_{5} (500) - \log_{5} (2^{2})$

Step 1.2

Raise $2$ to the power of $2$ .

$\log_{5} (500) - \log_{5} (4)$

Step 2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{5} (\frac{500}{4})$

Step 3

Logarithm base $5$ of $\frac{500}{4}$ is $3$ .

$3$